mit :: ai :: aim :: AIM-247

MASSACHUSETTS INSTITUTE OF TECHNOLOGY
A.I. LABORATORY

October 1971

Artificial Intelligence LOGO

Memo No. 247 Memo No. 2

TEACHING CHILDREN THINKING 1 ,2
Seymour Pa pert*

This report describes research done at the Artificial Intelligence Laboratory of
the Massachusetts Institute of Technology. Support for the laboratory's educa-
tion research is provided in part by the National Science Foundation under

grant fiJ-1049. *

*Th1s paper is deeply influenced by Cynthia Solomon and Marvin Mlnsky.

Presented at the Proceedings of IFIPS World Congress on Computers
and Education, Amsterdam, The Netherlands, 1970.

To be published in Mathematics Te aching (The Association of Teachers
of Mathematics, Leicester, England: 1972)-

This paper 1s dedicated to the hope that someone
with power to act will one day see that contemporary
research on education is like the following experiment
by a nineteenth century engineer who worked to demonstrate
that engines were better than horses. This he did
by hitching a 1/8 HP motor in parallel with his team
of four strong stallions. After a year of statistical
research he announced a significant difference. However,
It was generally thought that there was a Hawthorne effect
on the horses,

1. Introduction

The phrase "technology and education" usually means Inventing new
gadgets to teach the same old stuff in a thinly disguised version of
the same old way. Moreover, if the gadgets are computers, the same
old teaching becomes incredibly more expensive and biased towards Us
dullest parts, namely the kind of rote learning in which measurable
results can be obtained by treating the children like pigeons in a
Skinner box.

The purpose of this essay is to present a grander vision of an educa-
tional system in which technology is used not in the form of machines for
processing children but as something the child himself will learn to manip-
ulate, to extend, to apply to projects, thereby gaining a greater and more
articulate mastery of the world, a sense of the power of applied knowledge
and a self-confidently realistic image of himself as an intellectual agent.
Stated more simply, I believe with Dewey, Hontessori and Piaget that chil-
dren learn by doing and by thinking about what they do. And so the funda-
mental ingredients of educational fnnovation must be better things to do
and better ways to think about oneself doing these things.

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I claim that computation is by far the richest known source of these
ingredients. We can give children unprecedented power to invent and carry
out exciting projects by providing them with access to computers, with
a suitably clear and intelligible programming language and with periph-
eral devices capable of producing on-line real-time action.

Examples are; spectacular displays on a color
scope, battles between computer controlled
turtles, conversational programs, game-playing
heuristic programs, etc. Programmers can extend
the list indefinitely. Others can get the flavor
of the excitement of these ideas from movies I
shall show at the IFIPS meeting.

Thus in its embodiment as the physical computer, computation opens
a vast universe of things to do. But the real magic comes when this
is cootoined with the conceptual power of theoretical ideas associated
with computation.

Computation has had a profound impact by concretizing and elucidating
many previously subtle concepts in psychology, linguistics, biology, and
the foundations of logic and mathematics. I shall try to show how this
elucidation can be projected back to the initial teaching of these con-
cepts. By doing so much of what has been most perplexing to children
is turned to transparent simplicity; much of what seemed most abstract
and distant from the real world turns into concrete instruments famili-
arly cnployed to achieve personal goals.

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Mathematics Is the most extreme example. Most
children never see the point of the foraal use
of language. They certainly never have the experi-
ence of making their own formalism adapted to a
particular task. Yet anyone who works with a
computer does this all the time- We find that
terminology and concepts properly designed to
articulate this process are avidly seized by the
children who really want to make the computer
do things. And soon the children have beccme
highly sophisticated and articulate in the art
of setting up models and developing formal sys-
tems*
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The most important (and surely controversial) component of this impact
is on the child's ability to articulate the working of his own mind and
particularly the Interaction between himself and reality in the course
of learning and thinking. This is the central theme of this paper, and
I shall step back at this point to place It in the perspective of some
general ideas about education. We shall return later to the use of
computers.

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2. The Don't-Think-About-ThinMng Paradox

It is usually considered good practice to give people instruction in
their occupational activities. Now, the occupational activities of chil-
dren are learning, thinking, playing and the like. Yet, we tell them
nothing about those things. Instead, we tell them about numbers, granmar
and the French revolution; somehow hoping that from this disorder the really
Important things will emerge all by themselves. And they sometimes do.
But the alienation-dropout-drug complex is certainly not less frequent.

In this respect it is not a relevant innovation to teach children also
about sets and linguistic productions and Eskimos. The paradox remains:
why don't we teach them to think, to learn, to play? The excuses people
give are as paradoxical as the fact itself. Basically there are two*
Some people say: we know very little about cognitive psychology; we
surely do not want to teach such half-baked theories in our schools!
And some people say: making the children self-conscious about learning
will surely impede their learning. Asked for evidence they usually tell
stories like the one about a millipede who was asked which foot he moved
first when he walked. Apparently the attempt to verbalize the previously
unconscious action prevented the poor beast from ever walking again.

The paradox is not in the flimsiness of the evidence for these excuses.
There is nothing remarkable in that: all established doctrine about edu-
cation has similarly folksy foundations. The deep paradox resides in the

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curious assumption that our choice is this: either teach the children
half-baked cognitive theory or leave them in their original state of cog-
nitive innocence. Nonsense, The child does not wait with a virginally
empty mind until we are ready to stuff it with a statistically validated
curriculum. He is constantly engaged in inventing theories about every-
thing, including himself, schools and teachers- So the real choice is:
either give the child the best Ideas we can muster about cognitive pro-
cesses or leave him at the mercy of the theories he invents or picks up
in the gutter. The question is: who can do better, the child or us?
Let's begin by looking more closely at how well the child does.

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3, The Pop-Ed Culture

One reads in Piaget's books about children re-inventing a kind of
Democritean atomic theory to reconcile the dissappearance of the dissolv-
ing sugar with their belief in the conservation of natter. They believe
that vision 1s made possible by streams of particles sent out like machine
gun bullets from the eyes and even, at a younger age* that the trees make
the wind by flapping their branches. It is criminal to react (as some
do) to Piaget's findings by proposing to teach the children "the truth,"
For they surely gain more in their intellectual growth by the act of
inventing a theory than they can possibly lose by believing, for a while,
whatever theory they invent- Since they are not in the business of mak-
ing the weather, there is no reason for concern about their meteorologi-
cal unorthodoxy. But they are in the business of making minds—notably
their own—and we should consequently pay attention to their opinions
about how minds work and grow.

There exists amongst children, and in the culture at large, a set of
popular ideas about education and the mind. These seem to be sufficiently
widespread, uniform and dangerous tocfeserve a najne, and I propose " The
Pop^E d Culture .*" The following examples of Pop-Ed are taken from real
children. % samples are too small for me to guess at their prevalence.
But I am sure very similar trends must exist very widely and that identi-
fying and finding methods to neutralize the effects of Pop-Ed culture
will become one of the central themes of research on education.

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Examples of Pop-Ed Thinking

■
t fl ) Blank-Hind Theories . Asked how one sets about thinking a

child said: "make your mind a blank and wait for an idea to come."
This 1s related to the common prescription for memorizing: "keep
your mind a blank and say it over and over". There 1s a high corre-
lation, In ray small sample, between expressing something of this

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sort and complaining of inability to remember poetry!

(b) Getting-it Theories. Many children who have trouble understand-
ing mathematics also have a hopelessly deficient model of what mathe-
matical understanding is like. Particularly bad are models which
expect understanding to come in a flash, all at once, ready made.
This binary model is expressed by the fact that the child will admit
the existence of only two states of knowledge often expressed by
"I get it" and "I don't get It." They lack-and even reslst-a model
of understanding something through a process of additions, refine-
ments, debugging and so on. These children's way of thinking about
learning is clearly disastrously antithetical to learning any concept
that cannot *be acquired In one bite.

( c * Faculty Theories. Most children seen to have, and extensively
use, an elaborate classification of mental abilities: "he's a brain",
"he's a retard", "he's dumb", "I'm not mathematical-minded". The

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disastrous consequence Is the habit of reacting to failure by classi -
f y in g the problem as too hard, or oneself as not having the required

aptitude, rather than by diagnosing the specific deficiency of know-
ledge or skill.

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4. Computer Science as a Grade School Subject

Talking to children about all these bad theories is almost certainly
inadequate as an effective antidote* In common with

all the greatest thinkers in the philosophy of education I
believe that the child's intellectual growth must be rooted in his experi-
ence. So I propose creating an environment In which the child will
become highly involved in experiences of a kind to provide rich soil for
the growth of intuitions and concepts for dealing with thinking, learning*
playing, and so on. An exarcple of such an experience is writing simple
heuristic programs that play games of strategy or try to outguess a child
playing tag with a computer controlled "turtle".

Another, related example, which appeals enormously to some children
with whom we have worked is writing teaching programs- These are like
traditional CAI programs but conceived, written, developed and even tested
(on other children) by the children themselves.

(Incidentally, this is surely the proper use
for the concept of drlll-and-practlce programs-
Writing such programs is an ideal project for
* the second term of an elementary school course of
the sort I shall describe In a moment. It is
said that the best way to learn something is to
teach It. Perhaps writing a teaching program
is better still in its Inslstance on forcing one
to consider all possible misunderstandings and
Mistakes, I have seen children for whom doing

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arithmetic would have been utterly boring and
alienated becwne passionately involved in writing
programs to teach arithmetic and in the pros and
cons of criticisms of one another's programs like:
"Don't just tell him the right answer 1f he's
wrong, give him useful advice," And discussing
what kind of advice is "useful 11 leads deep into
understanding both the concept being taught and
the processes of teaching and learning.)

Can children do all this? In a moment I shall show some elements of
a programing language called LOGO, which we have used to teach children
of most ages and levels of academic performance how to use the computer.
The language is always used "on-line", that is to say the user sits at
a console, gives instructions tfl the tidchirte Artd imrtediately gets a
reaction. People who know languages can think of it as "baby LISP",
though this is misleading in that LOGO is a full-fledged universal lan-
guage. Its babyish feature fs the existence of self-contained sub-sets
that can be used to achieve some results after ten minutes of instruction.
Our most extensive teaching experiment was with a class of seventh grade
children (twelve year olds) chosen near the average in previous academic
record. Within three months these children could write programs to play
games like the simple form of NIM in which players take 1, 2, or 3 matches
from a pile; soon after that they worked on programs to generate random
sentences—like what is sometimes called concrete poetry--and went on
from there to make conversational and teaching programs. So the empiri-
cal evidence is very strong that we can do it, and next year we shall be
conducting a more extensive experiment with fifth grade children. The

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next sections wi 11 show some of the elementary exercises we shall use in
the first weeks of the course. They will also indicate another important
aspect of having children do their work with a computer: the possibility
of working on projects with enough duration for the child to become per-
sonally — Intellectually and emotionally—involved- The final section
will indicate a facet of how more advanced projects are handled and how
we see the effects of the kind of sophistication developed by the children-

5, You Can Take the Child to Euclid, But You Can't Make Him Think

Let's 90 back to Dewey for a moment. Intellectual growth,
he often told us, must be rooted In the child's experience, But
surely one of the fundamental problems of the school is how to extend
or use the child's experience. It must be understood that "experience"
does not mean mere busy work: two children who are made to measure
the areas of two triangles do not necessarily undergo the same ex-
perience. One might have been highly involved (e.g. anticipating
the outcome, being surprised, guessing at a general law) while the
other was quite alienated (the opposite). What can be done to in-
volve the mathematically alienated child? It is absurd to think
this can te done by using the geometry to survey the school grounds
instead of doing it on paper. Host children will enjoy running
about in the bright sun. But most alienated children will remain
alienated. One reason I want to emphasize here is that surveying the
school gro-nds is not a good research project on which one can work
for a long enough time to accumulate results and become Involved in
their development. There is a simple trick, which the child sees or
does not see. If he sees it he succeeds in measuring the grounds
and goes back to class the next day to work on something quite different.

Contrast this situation with a different context in which
a child might learn geometry. The child uses a time-shared computer
equipped with a CRT. He programs on-line in a version of the pro-
graming language LOGO, which will be described in more detail below.

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On the tube 1s a cursor point with an arrow Indicating a direction.
The instruction

FORWARD 100
causes the point to move in the direction of the arrow through 100
units of distance. The instruction

ROTATELEFT 90
causes the arrow to rotate 90°.

The child knows enough from previous experience to write
the following almost self-explanatory program:
TO CIRCLE
FORWARD 1
ROTATELEFT 1
CIRCLE
END

The word "TO" indicates that a new procedure 1s to be defined, and 1t
will be called "CIRCLE". Typing

CIRCLE
will now cause the steps In the procedure to be executed one at a time-
Thus;

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1 st Step:
2 nd Step:
3 rd Step:

FORWARD 1
ROTATELEFT 1
CIRCLE

The point creeps ahead 1 unit.

The arrow rotates 1°.

This is a recursive call;
naturally 1t has the same effect
as the conrond CIRCLE typed by
the child. That is to say,
it initiates the same process:

1 st Step
2 nd Step
3 rd Step

FORWARD 1
ROTATELEFT 1
CIRCLE

The point creeps on, but 1n the
new, slightly different direction.
The arrw now makes an angle of 2°
with Its initial direction.
This Initiates the same process
all over again. And so on, forever.

It 1s left as a problem for the reader to discover why this point

will describe a circle rather than, say, a spiral. He will find that

it involves some real geometry of a sort he may not yet have encountered

(See answer at end of paper.). The more immediately relevant point

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is that the child's work has resulted in a certain happening, namely

a circle has appeared. It occurs to the child to make the circle roll?

How can this be done? A plan 1s easy to make;

Let the point go round the circle once.

Then FORWARD 1

Then repeat.
But there is a serious problem! The program as written causes the point
to go round and round forever. To make it go just once round we need
to give the procedure an input (in more usual jargon: a variable).

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This input will be used by the procedure to remember how far round it

has gone. Let's call it "DEGREES" and let it represent the nunfcer of

degrees still to go. so it starts off being 360 and ends up 0. The

way this is written in LOGO is:

TO CIRCLE :0EGREES :DEGREES means: the thing whose name

is "DEGREES".
IF : DEGREES - STOP

FORWARD 1

ROTATE LEFT 1

CIRCLE :DEGREES - 1 Each time round the number of degrees

remaining is reduced by 1.

END

Now we can use this as a sub-procedure for ROLL:

TO ROLL

CIRCLE 360

FORWARD 10

ROLL

END
Or, to make it roll a fixed distance:

TO ROLL DISTANCE

*

IF : DISTANCE - STOP
CIRCLE 360 ,
FORWARD 10
ROLL : DISTANCE - 1
END
Or we can make the circle roll around a circle:

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TO FUNNYROLL
CIRCLE 360
FORWARD 10
ROTATELEFT 10
FUNNYROLL

These examples will* if worked on with a good dose of imagination,
Indicate the sense 1n which there are endless possibilities of creating
even more, but gradually more, complex and occasionally spectacularly
beautiful effects- Even an adult can get caught up in it! Not
e^ery child will. But if he does, the result is very likely to be
a true extension of his experience in Dewey's sense. And evidence
is accumulating for the thesis that there 1s scarcely any child who
cannot be involved in some computational project.

■
The next two sections will discuss two other peripheral devices

suitable for a computation laboratory in an elementary school: a

prograrmiable vehicle and a music generator. There is, of course, no

end to what one could invent. At M.I.T, we are thinking in terms of

soon adding mechanical manipulators, psychedelic light shows in a

reactive environment, apparatus for automated experiments in animal

psychology, etc., etc., etc..

6, The Love of the- Turilo

At M.I.Ti wt* use the name "Turtle" for snail computer controlled
vehicles, equipped with various kinds of sense, voice and writing organs*
Turtles can be controlled by the same conmands used In the previous
section to describe Graphics. They can be made to draw or to move
about without leaving a visible trace. Procedures to achieve this
are exactly like the procedures for CRT Graphics. However sense
organs allow another interesting dimension of work. An Interesting
simple one is a reflectivity sensor held close to the floor. A LOGO
operation called "LIGHT" has an integer value between Hflht

and 10, depending on the relfectivity of the surface.
Suppose we wish to program the turtle to follow
the left edge of a black line on a white floor.
Using an important heuristic we encourage the
child to study himself in the situation, and
try to simulate his own behavior. The key
idea, of course is to use feed-back accord-
ing to the following plan:

\7

SENSOR

photo-
i^** - detector

too far left

too far right

desired position